A Study on Labeling Problems in Signed Graphs

Title

A Study on Labeling Problems in Signed Graphs

Creator

Divya, Antoney

Contributor

Rajashekar, Paradesi Tabitha

Description

A signed graph can be considered as a weighted graph G; that is, edges of G have been given the weights + and and#8722;. We discuss two ways to assign signs to the vertices of a line signed graph of a signed graph, namely S-marking and Canonical marking (C-marking) of L(S). We characterize signed graphs whose line signed graphs are S-cordial or total S-cordial provided the vertices of L(S) receive signs through S-marking. Also, we characterize signed graphs whose line signed graphs are C-cordial or total C-cordial provided the vertices of L(S) receive signs through C-marking. Signed graphs can be eand#64256;ectively used to model relationships and individual preferences toward one another. To represent this scenario we defne a signed graph from a given graph. The colors of the vertices can be used to represent individuals or sets, and the signs on the edges of the graph represent the relationship between them. So, we defne two labelings of a properly colored graph, namely parity labeling of a properly colored graph and product labeling of a properly colored graph. newlineThe parity labeling of a properly colored graph G under and#967;(G) colors is defned by assigning the sign of the edge of G as + if the colors on the adjacent vertices of that edge are both even or both odd, and#8722; otherwise. The obtained signed graph is known as parity colored signed graph of a graph. We characterize signed graphs which admit parity coloring. We also characterized signed graphs whose line signed graphs admit parity coloring. We initiate the study on parity labeling of a properly colored graph and the chromatic rna number of a graph. Also, we defne product labeling of a properly colored graph. The product labeling of a properly colored graph G under and#967;(G) colors is defned by assigning the sign of the edge of G as + if the color of one of the incident vertex of that edge is even, and#8722; otherwise. The obtained signed graph is known as color product signed graph of a graph. We characterize signed graphs which admit color product coloring.

Source

Author's Submission

Date

2024-01-01

Publisher

Christ(Deemed to be University)

Subject

Mathematics and Statistics

Rights

Open Access

Relation

61000339

Format

PDF

Language

English

Type

PhD

Identifier

http://hdl.handle.net/10603/574684